Control theory has its roots in the use of feedback as a means to regulate physical processes and mediate the effect of modeling uncertainty and noise. Early on, in the latter part of the 18th century, the flyball centrifugal governor enabled effective speed control of the steam turbine and thereby shares credit for the industrial revolution. Ever since, control has played a key role as an “enabling technology” in applications ranging from autopilots, navigation and telecommunications, to manufacturing, and power systems. The closing of the 20th century saw a rapid development of the mathematics of systems, control and optimization with a focus placed on understanding the benefits and limitations of feedback.

The beginning of the 21st century is witnessing remarkable developments in computing, communications, and sensing technologies that present unprecedented opportunities to impact the economic and scientific development of the nation and the world. As a result, the scope of control theory is rapidly evolving to encompass hybrid and hierarchical data-driven decision-making with human-in-the-loop, distributed processes and networks where their connectivity at various scales affects functionality, and also to enable the probing and control of the microworlds of the quantum and of biology. The impetus of recent technological strides is driving the need for mathematics and rigor in addressing an ever expanding range of new challenges.

Please explore the tabs below to get a fuller description of the program -- the organizing committee, their vision for the year, and the workshops being planned. The IMA will select up to eight postdoctoral fellows to participate in the program.

The themes for the year have been selected from topics of current interest that are perceived to have the greatest promise for new developments, both with regard to the mathematics of control theory and in their impact on engineering applications. For each theme, the IMA will bring together mathematicians, theoretical engineers, and domain experts. Themes will typically begin with a one- to two-day tutorial by a small group of participants. There will be three overarching topics, each covering one trimester of the academic year. These are:

Dynamics and control on graphs and networks

Large-scale systems and PDEs: Modeling, optimization, and control

Control of the small and the large emergent applications

Full Description

Concepts and techniques from control theory are becoming increasingly interdisciplinary. At the same time, trends in modern control theory are influenced and inspired by other disciplines. As a result, the systems and control community is rapidly broadening its scope in a variety of directions. The IMA program is designed to encourage true interdisciplinary research and the cross fertilization of ideas. An important element for success is that ideas flow across disciplines in a timely manner and that the cross-fertilization takes place in unison.

Due to the usefulness of control, talent from control theory is drawn and often migrates to other important areas, such as biology, computer science, and biomedical research, to apply its mathematical tools and expertise. It is vital that while the links are strong, we bring together researchers who have successfully bridged into other disciplines to promote the role of control theory and to focus on the efforts of the controls community. An IMA investment in this area will be a catalyst for many advances and will provide the controls community with a cohesive research agenda.

In all topics of the program the need for research is pressing. For instance, viable implementations of control algorithms for smart grids are an urgent and clearly recognized need with considerable implications for the environment and quality of life. The mathematics of control will undoubtedly influence technology and vice-versa. The urgency for these new technologies suggests that the greatest impact of the program is to have it sooner rather than later.

First trimester (Fall 2015): Networks, whether social, biological, swarms of animals or vehicles, the Internet, etc., constitute an increasingly important subject in science and engineering. Their connectivity and feedback pathways affect robustness and functionality. Such concepts are at the core of a new and rapidly evolving frontier in the theory of dynamical systems and control. Embedded systems and networks are already pervasive in automotive, biological, aerospace, and telecommunications technologies and soon are expected to impact the power infrastructure (smart grids). In this new technological and scientific realm, the modeling and representation of systems, the role of feedback, and the value and cost of information need to be re-evaluated and understood. Traditional thinking that is relevant to a limited number of feedback loops with practically unlimited bandwidth is no longer applicable. Feedback control and stability of network dynamics is a relatively new endeavor. Analysis and control of network dynamics will occupy mostly the first trimester while applications to power networks will be a separate theme during the third trimester. The first trimester will be divided into three workshops on the topics of analysis of network dynamics and regulation, communication and cooperative control over networks, and a separate one on biological systems and networks.

The second trimester (Winter 2016) will have two workshops. The first will be on modeling and estimation (Workshop 4) and the second one on distributed parameter systems and partial differential equations (Workshop 5). The theme of Workshop 4 will be on structure and parsimony in models. The goal is to explore recent relevant theories and techniques that allow sparse representations, rank constrained optimization, and structural constraints in models and control designs. Our intent is to blend a group of researchers in the aforementioned topics with a select group of researchers with interests in a statistical viewpoint. Workshop 5 will focus on distributed systems and related computational issues. One of our aims is to bring control theorists with an interest in optimal control of distributed parameter systems together with mathematicians working on optimal transport theory (in essence an optimal control problem). The subject of optimal transport is rapidly developing with ramifications in probability and statistics (of essence in system modeling and hence of interest to participants in Workshop 4 as well) and in distributed control of PDE's. Emphasis will also be placed on new tools and new mathematical developments (in PDE's, computational methods, optimization). The workshops will be closely spaced to facilitate participation in more than one.

The third trimester (Spring 2016) will target applications where the mathematics of systems and control may soon prove to have a timely impact. From the invention of atomic force microscopy at the nanoscale to micro-mirror arrays for a next generation of telescopes, control has played a critical role in sensing and imaging of challenging new realms. At present, thanks to recent technological advances of AFM and optical tweezers, great strides are taking place making it possible to manipulate the biological transport of protein molecules as well as the control of individual atoms. Two intertwined subject areas, quantum and nano control and scientific instrumentation, are seen to blend together (Workshop 6) with partial focus on the role of feedback control and optimal filtering in achieving resolution and performance at such scales. A second theme (Workshop 7) will aim at control issues in distributed hybrid systems, at a macro scale, with a specific focus the “smart grid" and energy applications.